Frequency Regulation of a Hybrid Wind–Hydro Power Plant in an...

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Frequency Regulation of a Hybrid Wind–HydroPower Plant in an Isolated Power System

Guillermo Martínez-Lucas * ID , José Ignacio Sarasúa and José Ángel Sánchez-Fernández ID

Department of Hydraulic, Energy and Environmental Engineering, Universidad Politécnica de Madrid,C/Profesor Aranguren, 28040 Madrid, Spain; [email protected] (J.I.S.);[email protected] (J.Á.S.-F.)* Correspondence: [email protected]; Tel.: +34-910-674-333

Received: 13 December 2017; Accepted: 16 January 2018; Published: 19 January 2018

Abstract: Currently, some small islands with high wind potential are trying to reducethe environmental and economic impact of fossil fuels by using renewable resources.Nevertheless, the characteristics of these renewable resources negatively affect the quality of theelectrical energy, causing frequency disturbances, especially in isolated systems. In this study,the combined contribution to frequency regulation of variable speed wind turbines (VSWT) and apump storage hydropower plant (PSHP) is analyzed. Different control strategies, using the kineticenergy stored in the VSWT, are studied: inertial, proportional, and their combination. In general,the gains of the VSWT controller for interconnected systems proposed in the literature are notadequate for isolated systems. Therefore, a methodology to adjust the controllers, based on exhaustivesearches, is proposed for each of the control strategies. The control strategies and methodology havebeen applied to a hybrid wind–hydro power plant on El Hierro Island in the Canary archipelago.At present, in this isolated power system, frequency regulation is only provided by the PSHPand diesel generators. The improvements in the quality of frequency regulation, including theVSWT contribution, have been proven based on simulating different events related to wind speed,or variations in the power demand.

Keywords: wind–hydro systems; variable speed wind turbine; governor tuning; wind turbinefrequency regulation; inertia emulation

1. Introduction

The increased use of intermittent renewable energy sources in most electric power systems hasbeen documented [1,2]. These increases constitute a good way to reduce polluting gases generated byfossil fuel combustion. However, this class of renewable energies involves inherent drawbacks, such asunpredictability [3] or demand independence [4]. These characteristics of renewable sources negativelyaffect the quality of the supplied electrical energy, causing frequency [5] and power disturbances [6].

According to Albadi and El-Saadany [3], the impact of renewable energies on power systemsdepends mainly on its penetration rate and the system inertia. For this reason, the negative effectsof renewable energy sources are amplified in isolated systems. Nevertheless, in islands with windpotential, the economic and environmental costs of fossil fuels can be reduced. Therefore, the reduceduse of fossil fuels owing to the increasing use of renewable energies in small isolated systems hasbecome the main focus of numerous researchers during the past few years [7–10]. For example,Kaneshiro [11] has analyzed how wind ramps affect the quality of supply in a Hawaiian powersystem, considering different rates of renewable penetration and highlighting the importance ofwind forecasting in the medium and long term in order to operate the system safely and efficiently.In [12], the penetration of wind energy in Flores Island has been shown to be limited because of

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Energies 2018, 11, 239 2 of 25

low-frequency problems. According to [13], the increased penetration of wind and solar energy inthe power systems of the French islands of Martinique and Réunion has generated serious problemsof frequency deviations, thereby establishing load shedding operations as common operations forall these power systems. In fact, the French government—by ministerial order—has limited thepenetration of renewable sources in power systems to 30%.

Different methods exist in the literature that mitigate these negative effects. In [6], a penaltysystem has been introduced for generators that cause frequency disturbances. Energy storage cancontribute to this aim. Others [14,15] have carried out exhaustive reviews of available energy storagetechnologies in the last few years, remarking on the importance of pump storage hydropower plants(PSHP), flywheels, batteries, capacitors, or superconductors. Specifically, in the case of isolated systems,it has been shown that the long-term variability of renewable energy is well managed by combiningwind and solar farms with PSHPs [16–18]. However, in the short term, PSHPs need complementarytechnologies capable of injecting or absorbing power over brief time periods of a few seconds to avoidinadmissible frequency variations [15,19,20]. These contributions to frequency regulations can beprovided by flywheels [21,22], variable-speed hydro-pump turbines [23], and others.

Variable-speed wind turbines (VSWT) can also provide frequency regulation to mitigate largefrequency deviations after disturbances [24]. Several approaches can be found in the literature on thecontributions of frequency support to the regulation of wind turbines [25,26]. In general, VSWT providenegligible inertia since the fast control of power electronic converters maintains a practically constantoutput power irrespective of changes in the frequency of the grid [27]. However, it is possible toachieve short-term inertial responses from variable-speed wind turbines by modifying their controlloops [28–31]. According to this idea, synthetic inertia of a VSWT is modeled in [32], highlighting theimportant improvement in the minimum frequency (NADIR). Different activation schemes for thesynthetic inertia on VSWT based on full converters have been proposed in [33]. The same authors haveestablished the practical limits of synthetic inertial gains in the inertia controller used in full-converterVSWT generators in [34].

Primary frequency regulation can also be provided by VSWT. The primary frequency responsestabilizes the frequency at a new value by modifying the power generation proportionally to differentfrequency variations. Admittedly, a non-optimal working point can be reached in the responsecurve of torque and rotor speed of the turbine [35,36]. Furthermore, the impact of using doubly fedinduction wind generators participating in primary frequency regulation has been evaluated in [37–39].Moreover, primary frequency regulation can be combined with inertia emulation [40,41]. In [42],a control loop acting on the frequency deviation is added to the inertia emulation loop in order toenhance the inertia support from the wind turbine, maintaining a permanent frequency error.

The main problem of the contribution of VSWT to the primary regulation is that VSWT do notoperate at their optimum operational point. This non-optimal operation would reduce the generatedenergy to some extent, and inevitably leads to economic losses [43]. To mitigate this drawback,Mauricio et al. [44] have presented a new method to improve the use of variable-speed wind energyconversion systems by modifying the inertial control scheme through the addition of a proportionalloop that weights the frequency deviation. Both classical and modified inertial control loops allow therelease of the stored fraction of the kinetic energy in rotational masses to provide earlier frequencysupport, thereby taking advantage of the fast response capability of electronically controlled converters.This control strategy does not need to have a regulation reserve, and thus allows a better use ofwind resources.

The aim of this study is to evaluate the VSWT contribution to frequency regulation in anisolated power system when it operates solely based on the use of wind and hydro resources.Different control strategies for the VSWT are analyzed: inertial, proportional, and their combination.Primary regulation is not considered adequate in avoiding the negative economic effects associatedwith VSWT. The VSWT controller gains that have been proposed in the literature have been previouslyemployed in interconnected systems, but these settings may not be adequate for isolated systems.

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Therefore, new controller adjustments will be used herein for each control strategy based on anexhaustive search. Additionally, this study has also analyzed whether it is necessary to modify thePSHP governor settings owing to the VSWT contribution to frequency regulation.

To achieve these objectives, a dynamic model has been developed. The construction of a realisticmodel that takes into account all the phenomena involved in system operations is essential in order todraw relevant conclusions [45]. The PSHP configuration includes a large penstock, thereby limiting theapplicability of rigid-water column models, and making it necessary to consider elastic phenomena [46].In order to model the VSWT properly, the VSWT speed governor, VSWT inertial control loop,VSWT blade pitch angle control, and VSWT aerodynamics, have been used.

Control strategies and adjustment methodology extracted from this study are appliedto the El Hierro power system. El Hierro is an island in the Canary island archipelago.Historically, electric generation was based on diesel generators. The island aims to become entirelyfree from carbon dioxide emissions [9]. In order to contribute to the achievement of this objective,a power hybrid wind–pumped storage hydropower plant (W-PSHP) at a rated power of 22.8 MW wascommitted in June 2014 to minimize utilization of fossil fuels [47]. As a matter of fact, the electricalenergy generated in 2015 by the W-PSHP in Gorona del Viento was 9 GWh, which corresponded to22.5% of the total electrical energy demand in the island. During 2015, the maximum power demandwas 7.7 MW. In fact, only just 1000 h of operation have been achieved since the onset of 100% renewablegeneration [48]. This underutilization of renewable resources may have been caused by inadmissiblefrequency deviations. Although the inertia and the regulation capacity of PSHP are insufficient to elicitadequate responses to the fluctuations in demand and wind generation, the regulation capacity of theVSWT is currently not used. It is expected that frequency deviations will be reduced owing to thecontribution of VSWT to frequency regulation, thereby approaching the fulfilment of the objective ofoperating the island with 100% renewable energy.

The paper is organized as follows. In Section 2, the W-PSHP dynamic model is presented.The VSWT control loops and the control strategy are described in Section 3. The methodology used toadjust the VSWT control loop gains based on an exhaustive search is proposed in Section 4. In Section 5,some realistic events applied to El Hierro power system are proposed to simulate the W-PSHP dynamicresponse so as to evaluate the proposed methodology. Finally, Section 6 outlines the main conclusionsof this study.

2. Hybrid Wind–Hydro Power Plant Simulation Model Description

A PSHP and a VSWT connected to an isolated system have been modeled in MATLAB (TechnicalUniversity of Madrid license) with Simulink. Frequency regulation will be provided by the VSWTand the PSHP. Therefore, the simulation model includes the dynamic behavior of an isolated powersystem, a PSHP and a VSWT. PSHP will operate in generation mode during all simulations. The VSWTconverter dynamics and the PSHP alternator are supposed to be very fast when compared with theother components of the model. Therefore, the PSHP alternator and the VSWT converter dynamicswill be neglected, and the VSWT inertia is thus uncoupled from the electric system. Figure 1 shows theblock diagram of the hybrid wind–hydro power plant and the power system.

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Figure 1. Block diagram of the power system with a hybrid wind–hydro plant and the power system.

2.1. Power System

As stated above, the PSHP is connected to an isolated system comprising intermittent energy

sources and loads. Therefore, the frequency dynamics described by Equation (1) are the result of the

imbalance between the sum of the hydroelectric ph and wind converter powers pnc and the power

demand pdem.

1∆ (1)

Inertial mechanical time refers only to PSHP. VSWT is supposed to be connected to the system

through a frequency converter, and does not contribute to the system inertia. The parameter k

includes the load frequency sensitivity. It is assumed that k = 1, which corresponds to static loads.

2.2. Pumped Storage Hydropower Plant

A PSHP plant has been modeled with a long penstock in generation mode. Due to the length of

the penstock, the elasticity of water and conduit is needed to be considered. All the variables,

parameters, and coefficients used are explained in the nomenclature section.

2.2.1. Penstock

Transient flow in conduits is described by the conservation of mass and momentum (Equations

(2) and (3)) [49]:

0 (2)

0. (3)

To solve these equations, different approaches can be found in the specialized literature, such as

the method of characteristics [50], or the transfer function proposed in [51]. The lumped parameter

approach [52,53] has been used in this study to solve Equations (2) and (3).

Figure 1. Block diagram of the power system with a hybrid wind–hydro plant and the power system.

2.1. Power System

As stated above, the PSHP is connected to an isolated system comprising intermittent energysources and loads. Therefore, the frequency dynamics described by Equation (1) are the result of theimbalance between the sum of the hydroelectric ph and wind converter powers pnc and the powerdemand pdem.

Tmdndt

=1n(ph + pnc − pdem)− k∆n (1)

Inertial mechanical time refers only to PSHP. VSWT is supposed to be connected to the systemthrough a frequency converter, and does not contribute to the system inertia. The parameter k includesthe load frequency sensitivity. It is assumed that k = 1, which corresponds to static loads.

2.2. Pumped Storage Hydropower Plant

A PSHP plant has been modeled with a long penstock in generation mode. Due to the lengthof the penstock, the elasticity of water and conduit is needed to be considered. All the variables,parameters, and coefficients used are explained in the nomenclature section.

2.2.1. Penstock

Transient flow in conduits is described by the conservation of mass and momentum(Equations (2) and (3)) [49]:

∂H∂t

+aw

2

gS∂Qp

∂x= 0 (2)

1gS

∂Qp

∂t+

∂H∂x

+ fQp|Qp|2gDS2 = 0. (3)

To solve these equations, different approaches can be found in the specialized literature, such asthe method of characteristics [50], or the transfer function proposed in [51]. The lumped parameterapproach [52,53] has been used in this study to solve Equations (2) and (3).

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This approach leads to a system of ordinary differential equations that can be represented as aseries of consecutive, Γ-shaped elements where the conduit properties (inertia, elasticity, and friction)are proportionally assigned to the segment length Le. The ‘configuration’ and ‘orientation’ of theΓ-shaped elements may vary according to the upstream and downstream boundary conditions ofthe pipe. Figure 2 shows the scheme of the penstock model. Equations (4) and (5) of the penstockdynamics are

dhidt

= ntTw

Te2 (qp,i − qp,i+1) (4)

dqp,i

dt=

nt

Tw

(hi − hi+1 −

r2nt

qp,i∣∣qp,i

∣∣). (5)

Tw represents the water starting time, as defined in Equation (6) [54]:

Tw =L

gSQbHb

. (6)

The number of segments nt determines the order of the system.

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This approach leads to a system of ordinary differential equations that can be represented as a

series of consecutive, Γ‐shaped elements where the conduit properties (inertia, elasticity, and friction)

are proportionally assigned to the segment length Le. The ‘configuration’ and ‘orientation’ of the Γ‐

shaped elements may vary according to the upstream and downstream boundary conditions of the

pipe. Figure 2 shows the scheme of the penstock model. Equations (4) and (5) of the penstock

dynamics are

, , (4)

,, , . (5)

Tw represents the water starting time, as defined in Equation (6) [54]:

. (6)

The number of segments nt determines the order of the system.

Figure 2. Scheme of the penstock model.

2.2.2. Turbine

Equation (7) expresses the relation between flow, head, and nozzle opening [51], while Equation

(8) expresses the generated power corresponding to ideal rated conditions in Pelton turbines where

the absolute fluid speed is twice the runner peripheral speed [55]. Pelton turbines are widely used in

hydropower plants with high head available.

√ (7)

2√ (8)

The modeled hydropower plant has more than one identical unit. These units are supposed to

operate at the same time in an identical manner. Thus, a single equivalent turbine has been used

instead in the remaining parts of this work.

2.3. Variable Speed Wind Turbine Model

2.3.1. Wind Power Model

The power extracted from the wind is modeled using the mathematical function in Equation (9)

[56,57]:

, , (9)

where λ is the ratio of the rotor blade tip speed and the wind speed (10), while θ is the blade pitch

angle in degrees.

Ω (10)

Cp is usually provided as a group of curves that relates Cp to λ and θ. Equation (11) represents

the curves used in this model [57]. The Cp curves for the modeled wind turbine are shown in Figure

3a. These curves are a good approximation for values of 2 < λ < 13. Cp values corresponding to λ

smaller than the previous range have been linearly interpolated between Cp (λ = 0) and Cp (λ = 2).

Figure 2. Scheme of the penstock model.

2.2.2. Turbine

Equation (7) expresses the relation between flow, head, and nozzle opening [51], while Equation (8)expresses the generated power corresponding to ideal rated conditions in Pelton turbines where theabsolute fluid speed is twice the runner peripheral speed [55]. Pelton turbines are widely used inhydropower plants with high head available.

q = z√

h (7)

ph = qn(2√

h− n) (8)

The modeled hydropower plant has more than one identical unit. These units are supposed tooperate at the same time in an identical manner. Thus, a single equivalent turbine has been usedinstead in the remaining parts of this work.

2.3. Variable Speed Wind Turbine Model

2.3.1. Wind Power Model

The power extracted from the wind is modeled using the mathematical function inEquation (9) [56,57]:

Pwind =ρ

2Arsw

3Cp(λ, θ), (9)

where λ is the ratio of the rotor blade tip speed and the wind speed (10), while θ is the blade pitchangle in degrees.

λ =ΩRbsw

(10)

Cp is usually provided as a group of curves that relates Cp to λ and θ. Equation (11) represents thecurves used in this model [57]. The Cp curves for the modeled wind turbine are shown in Figure 3a.These curves are a good approximation for values of 2 < λ < 13. Cp values corresponding to λ

Energies 2018, 11, 239 6 of 25

smaller than the previous range have been linearly interpolated between Cp (λ = 0) and Cp (λ = 2).However, λ values outside the previous range represent either very high or low wind speeds thatare outside the continuous rating of the machine. These considerations are also outside the scope ofthis work.

Cp(λ, θ) =4

∑i=0

4

∑j=0

αi,jθiλj (11)

The values of the coefficient αij are listed in Table A1 in Appendix A.

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However, λ values outside the previous range represent either very high or low wind speeds that are

outside the continuous rating of the machine. These considerations are also outside the scope of this

work.

𝐶𝑝(𝜆, 𝜃) = ∑ ∑ 𝛼𝑖,𝑗𝜃𝑖𝜆𝑗

4

𝑗=0

4

𝑖=0

(11)

The values of the coefficient αij are listed in Table A1 in Appendix A

(a) (b)

Figure 3. (a) Wind power 𝐶𝑝(𝜆, 𝜃) curves; (b) Comparison between Cp (red) and power (blue)

responses resulting from the model (continuous lines) and response provided by the manufacturer

(dashed line) [58].

In order to check the validity of the Cp curves (Equation (11)), real data from a manufacturer [58]

have been used. As can be seen in Figure 3b, both the Cp curve and the generated power curve

obtained by the dynamic simulation model matched approximately those provided by the

manufacturer.

2.3.2. Blade Pitch Angle Control

Figure 4 shows the block diagram of the blade pitch angle control. This control is a combination

of a traditional pitch angle control and pitch compensation. The traditional pitch angle control

implements Proportional Integral (PI) control that computes the difference between rotor and

reference rotor speeds [59]. Furthermore, pitch angle control takes into account the compensation

through a different PI control that computes the difference between mechanical wind power and

maximum rated power for each wind speed [60].

Figure 4. Block diagram of pitch control model.

Figure 3. (a) Wind power Cp(λ, θ) curves; (b) Comparison between Cp (red) and power (blue) responsesresulting from the model (continuous lines) and response provided by the manufacturer (dashedline) [58].

In order to check the validity of the Cp curves (Equation (11)), real data from a manufacturer [58]have been used. As can be seen in Figure 3b, both the Cp curve and the generated power curve obtainedby the dynamic simulation model matched approximately those provided by the manufacturer.


Figure 4 shows the block diagram of the blade pitch angle control. This control is a combinationof a traditional pitch angle control and pitch compensation. The traditional pitch angle controlimplements Proportional Integral (PI) control that computes the difference between rotor and referencerotor speeds [59]. Furthermore, pitch angle control takes into account the compensation through adifferent PI control that computes the difference between mechanical wind power and maximum ratedpower for each wind speed [60].

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Energies 2018, 11, 239 6 of 24

However, λ values outside the previous range represent either very high or low wind speeds that are

outside the continuous rating of the machine. These considerations are also outside the scope of this

work.

, , (11)

The values of the coefficient αij are listed in Table A1 in Appendix A

(a) (b)

Figure 3. (a) Wind power , curves; (b) Comparison between Cp (red) and power (blue)

responses resulting from the model (continuous lines) and response provided by the manufacturer

(dashed line) [58].

In order to check the validity of the Cp curves (Equation (11)), real data from a manufacturer [58]

have been used. As can be seen in Figure 3b, both the Cp curve and the generated power curve

obtained by the dynamic simulation model matched approximately those provided by the

manufacturer.


Figure 4 shows the block diagram of the blade pitch angle control. This control is a combination

of a traditional pitch angle control and pitch compensation. The traditional pitch angle control

implements Proportional Integral (PI) control that computes the difference between rotor and

reference rotor speeds [59]. Furthermore, pitch angle control takes into account the compensation

through a different PI control that computes the difference between mechanical wind power and

maximum rated power for each wind speed [60].


2 4 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

0.5=0º

=1º

=2º

=3º

=4º

=5º

=6º

=7º

=8º

=9º

=10º

=11º

=12º=13º

=14º=15º

=16º

0 5 10 15 20 25Wind speed (m/s)

0

300

600

900

1200

1500

1800

2100

2400

0

0.1

0.2

0.3

0.4

0.5

0.6


The reference speed ωref is usually 1.2 p.u. but it can be lower. Speed reference is incorporatedin the model by using the quadratic equation, which has been obtained by taking into account theoperational curves provided by the manufacturers [58].

2.3.3. Mechanical Model of Rotor

The VSWT model includes the rotor inertial expression for the wind turbine rotor (12) [31].This expression computes the rotor speed variances owing to differences between the torque providedby the wind torque and the torque demanded by the power converter:

dω

dt=

12Hwt

1ω(pw − pnc). (12)

3. Proposed Hybrid Wind–Hydro Contribution to Frequency Regulation

In addition to the frequency regulation, usually provided by the hydroelectric power plant,the regulation capacity of the VSWT will be used. In this study, different VSWT control strategiesare analyzed in addition to hydropower frequency regulation. VSWT can contribute to frequencyregulation through different control strategies: inertial, proportional, and their combination. In thefollowing section, the PSHP governor and the VSWT control loops are described. Moreover, a windrotor speed control is necessarily included to make the VSWT restore the reference rotor speed;otherwise, the VSWT will be destabilized. Figure 5 shows the block diagram of the hybridwind–hydro controllers.

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Energies 2018, 11, 239 7 of 24

The reference speed ωref is usually 1.2 p.u. but it can be lower. Speed reference is incorporated in

the model by using the quadratic equation, which has been obtained by taking into account the

operational curves provided by the manufacturers [58].

2.3.3. Mechanical Model of Rotor

The VSWT model includes the rotor inertial expression for the wind turbine rotor (12) [31]. This

expression computes the rotor speed variances owing to differences between the torque provided by

the wind torque and the torque demanded by the power converter:

. (12)

3. Proposed Hybrid Wind–Hydro Contribution to Frequency Regulation

In addition to the frequency regulation, usually provided by the hydroelectric power plant, the

regulation capacity of the VSWT will be used. In this study, different VSWT control strategies are

analyzed in addition to hydropower frequency regulation. VSWT can contribute to frequency

regulation through different control strategies: inertial, proportional, and their combination. In the

following section, the PSHP governor and the VSWT control loops are described. Moreover, a wind

rotor speed control is necessarily included to make the VSWT restore the reference rotor speed;

otherwise, the VSWT will be destabilized. Figure 5 shows the block diagram of the hybrid wind–

hydro controllers.

Figure 5. Block diagram of the hybrid wind–hydro controllers.

3.1. PSHP Governor

The proposed PSHP governor model, which is based on [45], is formulated in Equation (13). The

main function of this regulator is to control the unit speed through the feedback frequency error

signal, modifying the turbine nozzles and regulating the water flow through the penstock. The error

signal is processed by a conventional proportional–integral (PI) controller. The limits in the positions

Figure 5. Block diagram of the hybrid wind–hydro controllers.

3.1. PSHP Governor

The proposed PSHP governor model, which is based on [45], is formulated in Equation (13).The main function of this regulator is to control the unit speed through the feedback frequency errorsignal, modifying the turbine nozzles and regulating the water flow through the penstock. The errorsignal is processed by a conventional proportional–integral (PI) controller. The limits in the positionsof the turbine nozzles and their rates of change are considered in the model by the use of a rate limiterand a saturator element.

∆z =

[1δ+

1δTr

∫dt](nre f − n) (13)

3.2. VSWT Inertial and Proportional Control Loop

Synthetic inertia is defined in [31] as ‘the response of a generating unit to frequency changes,and in particular, a power exchange that is proportional to Rate of Change of Frequency (RoCoF)’.Equation (14) represents the inertial control loop:

∆pdn = Kdnddt(nre f − n). (14)

The same authors have also defined ‘fast frequency response’ as the controlled contribution ofelectrical power from a unit that quickly corrects frequency deviations. Equation (15) represents theproportional control loop:

∆ppn = Kpn(nre f − n). (15)

Therefore, three control strategies can be defined. Inertial control strategy only takes the RoCoFas the control loop input. Proportional control strategy only takes the variation in frequency as thecontrol loop input. Finally, inertial and proportional control strategy takes both variations as thecontrol loop input.

Energies 2018, 11, 239 9 of 25

These inertial and proportional control loops allow a fraction of the kinetic energy stored inrotational masses to be released in order to provide earlier frequency support, thereby taking advantageof the fast response capability associated with electronically controlled converters. These controlstrategies allows not have a regulation reserve so a better use of the wind resource is achieved.

Owing to the existence of a wind energy conversion system, the inertial and proportional controlloops add a power signal ∆pn to the power reference output to be tracked by the converter (16) [44].

∆pn = ∆pdn + ∆ppn (16)

Kpn weighs the frequency deviation, while Kdn is a constant weighing of the frequency variationrate. When inertial or proportional control is executed individually, the other controller is disabled bycanceling the corresponding gain listed in Equations (14) and (15).

A methodology to adjust gain values is described in the following section. In practice, the valueof Kdn is limited given its relationship with the inertial constant of the real wind turbine, Hwt [34].This limitation has been used for its estimation.

3.3. VSWT Rotor Speed Control

The speed control, which controls the rotational speed by regulating the electromagnetic torque,aims to recover the optimal speed once the frequency transient has subsided [61]. Rotational speedcontrol is more convenient than pitch control when the rotational speed is below the maximumvalue [59]. Therefore, a PI controller obtains a power reference, ∆pω (17), based on the differencebetween the rotational speed and the optimal rotational speed. The PI controller proposed in this studyis based on [44]. The speed control must always be enabled; otherwise the VSWT will be destabilized.

∆pω =

[Kpω + Kiω

∫dt](ω−ωre f ) (17)

The total power supplied by the electronic converter (Equation (18)) will be the sum of themechanical power initially produced by the wind and both of the power increments that have beenpreviously described:

pnc = pnc0 + ∆pn + ∆pω. (18)

4. Controllers Adjustment Methodology

A methodology based on exhaustive searches is proposed for the adjustment of the PSHP andVSWT controller gains for each of the strategies described above. The benefits of the adjustments ofthe PSHP and VSWT controllers used together or individually were also analyzed. To achieve thesestrategies, two cases were considered: (1) known gains for the PSHP controller were assumed, and thegains of the VSWT controllers were then obtained, and (2) a search was conducted for all the controllergains. In order to obtain the PSHP governor gains and assess the contribution of the VSWT regulation,a strategy was considered in which VSWT did not provide frequency regulation, classified under‘case A’.

Blade pitch angle variations are slow enough to be decoupled from the dynamic responses of othervariables. In the literature, there is agreement on the value of these gains. Therefore, gains proposedin [56,57] have been assumed. Blade pitch angle control parameters are summarized in Table A2 inAppendix A.

Taking into account the casuistry described previously, seven different cases for the exhaustivesearches are distinguished. These cases are summarized in Table 1.

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Table 1. Exhaustive summary of search cases.

Strategy Case PSHP Adjustable Gains VSWT Adjustable Gains

Regulation is only provided by PSHP A δ, Tr -

VSWT inertial controlB -

Kdn, Kpw, KiwC δ, Tr

VSWT proportional controlD -

Kpn, Kpw, KiwE δ, Tr

VSWT inertial and proportional controlF -

Kdn, Kpn, Kpw, KiwG δ, Tr

For cases B, D, and F, the PSHP governor gains obtained in case A were assumed. To obtainPSHP governor gains and VSWT controller gains for the cases described previously, several exhaustivesearches had been carried out by varying the PSHP and VSWT controller gains when a 5% step increasein the load of the island had been simulated, according to the recommendation in [62] for the speedgovernor of hydraulic turbines.

For each studied case, at least two different wind speeds should be considered for the exhaustivesearch representing high and low wind speeds, thus assessing the VSWT operating point influenceon the adjustment of the controllers. Gains bounds are summarized in Table 2. It was assumed thatone equivalent turbine and one VSWT were operating. It has been verified that gains outside of thesebounds can destabilize the system.

Table 2. Gains bounds based on the exhaustive search conducted.

Gain Minimum Value Maximum Value

δ 0.5 5.0Tr 0.5 5.0

Kdn 0.5 6.0Kpn 0.5 6.0Kpw 0.1 1.0Kiw 0.005 0.010

NADIR, the settling power time, or settling frequency time, are technical indicators that are usedto define the system’s warranted frequency operating region from the unwarranted when an instantvariance in the power demand takes place. These frequency response indicators can be used in anynetwork to assess the frequency response owing to a loss of a generator [63]. In this case, the settlingfrequency time (Tn) is defined as the time it takes for the frequency to lie within the normal limitsestablished by the Transmission System Operator (TSO) for isolated systems [64]. The settling powertime (Tp) is defined as the time it takes for the power supplied by the VSWT and PSHP to be within±2% of the power demand value.

It is difficult to find a group of controller gains that jointly provide the best values for theseindicators. In the effort to achieve a compromising solution that improves these quality indicators,a coefficient has been proposed that favored increased NADIR values and penalized increased valuesfor both settling times. This coefficient is expressed in accordance with Equation (19):

ϕ =NADIRTn·Tp

. (19)

Therefore, NADIR, frequency settling time, power settling time, and the coefficient ϕ are usedto characterise the quality of the system’s response. Adjustment criterion is defined as that aimed to

Energies 2018, 11, 239 11 of 25

extract the VSWT and PSHP controller gains based on the exhaustive searches, thereby yielding thebest value of the coefficient ϕ.

5. Simulations and Results

Control strategies and adjustment methodology extracted from this study are applied to the ElHierro power system.

5.1. Case Study: El Hierro Power System

El Hierro is an island in the Canary island archipelago that was declared a biosphere reserveby United Nations Educational, Scientific and Cultural Organization (UNESCO). The island aimsto become 100% free from carbon dioxide emissions [9]. The electrical capacity of the islandis 35.9 MW, contributed by diesel generators (13 MW), solar farms (0.03 MW), and a W-PSHPrated at a power of 22.8 MW. The PSHP generates 11.32 MW, and the five VSWT provide theremaining 11.48 MW [65]. The electrical energy generated in 2015 by the Gorona del VientoW-PSHP was 9 GWh. This corresponded to 22.5% of the total electrical energy demand of the island.The maximum peak demand in that year was 7.7 MW, while the minimum was approximately4 MW [66]. Nowadays, only 1000 h of plant operation have been achieved since the onset of powergeneration using 100% renewable sources in June 2014 [48]. Currently, the VSWT are not assignedto contribute to frequency regulation. Therefore, as the PSHP inertia and regulation capacity areinsufficient to respond to the power demand and wind power fluctuations, a contribution fromdiesel generators is required to achieve frequency regulation. It is expected that the percentage ofdemand supplied by renewable resources will be increased. Thus, the number of hours of operationrequired to establish the island as self-sufficient based on the use of 100% renewable sources maybe increased proportionally. In this context, it is assumed that the W-PSHP operates in isolation.Therefore, variations in power demand and wind power fluctuations are balanced by the VSWT itselfand by the operation of the PSHP.

Data from the W-PSHP in Gorona del Viento used in the model have been obtained from [58,67,68].They are summarized in Table 3.

Table 3. Gorona del Viento W-PSHP ratings.

PSHP generating unit

Rated power 2.830 MWRated flow 0.5 m3/s

Number of units 4Rated speed 1000 rpm

Mechanical starting time (Tm) 6 sGross head 670 m

PSHP penstock

Length 2577 mDiameter 1 m

Darcy–Weisbach friction loss coefficient 0.015Wave speed (aw) 1193 m/sElastic time (Te) 2.16 s

VSWT

Number of VSWT 5Model ENERCON E-70 [58]

Rated power 2.3 MWBlade radius 35.5 m

Wind turbine inertia constant (Hwt) 1.971 p.u.

5.2. Adjustment of Control Strategies

Prior to checking the adequacy of the proposed methodology, it has been proven that theVSWT controller gains proposed in [44] for interconnected systems are not adequate for an isolated

Energies 2018, 11, 239 12 of 25

system, as shown in Figure 6, since isolated systems are more sensitive to power disturbances thaninterconnected systems.

Energies 2018, 11, 239 11 of 24

Model ENERCON E‐70 [58]

Rated power 2.3 MW

Blade radius 35.5 m

Wind turbine inertia constant (Hwt) 1.971 p.u.

5.2. Adjustment of Control Strategies

Prior to checking the adequacy of the proposed methodology, it has been proven that the VSWT

controller gains proposed in [44] for interconnected systems are not adequate for an isolated system,

as shown in Figure 6, since isolated systems are more sensitive to power disturbances than

interconnected systems.

Figure 6. System response owing to a 5% step in power demand assuming the inertial control gains

proposed in [44] for ws = 10 m/s.

Table 4 list the results of the exhaustive searches and response indicators for all the cases

proposed previously for representative wind speeds of 10 m/s and 20 m/s, when a 5% power demand

step is imposed.

Table 4. Exhaustive search results.

Case ws

Controllers GainsFrequency Response Indicators

PSHP VSWT

δ Tr Kdn Kpn Kpw Kiw NADIR Tn Tp

(m/s) (Hz) (s) (s)

A 10 0.70 2.00 ‐ ‐ ‐ ‐ 49.08 21.95 47.93 0.047

20 0.60 3.60 ‐ ‐ ‐ ‐ 49.06 9.93 63.19 0.078

B 10 0.70 2.00 0.50 ‐ 1.00 0.015 49.09 23.19 43.85 0.048

20 0.60 3.60 0.50 ‐ 0.10 0.025 49.08 11.34 53.34 0.081

C 10 0.50 1.90 1.50 ‐ 0.10 0.030 49.31 25.26 34.93 0.056

20 0.50 1.90 3.50 ‐ 0.10 0.005 49.41 15.80 37.23 0.084

D 10 0.70 2.00 ‐ 4.00 0.10 0.010 49.59 9.64 37.22 0.138

20 0.60 3.60 ‐ 4.00 0.80 0.010 49.56 16.38 36.46 0.083

E 10 3.50 0.30 ‐ 5.00 0.10 0.005 49.62 8.51 19.23 0.303

Figure 6. System response owing to a 5% step in power demand assuming the inertial control gainsproposed in [44] for ws = 10 m/s.

Table 4 list the results of the exhaustive searches and response indicators for all the cases proposedpreviously for representative wind speeds of 10 m/s and 20 m/s, when a 5% power demand stepis imposed.

Table 4. Exhaustive search results.

Casews

Controllers GainsFrequency Response Indicators

PSHP VSWT

δ Tr Kdn Kpn Kpw KiwNADIR Tn Tp ϕ

(m/s) (Hz) (s) (s)

A10 0.70 2.00 - - - - 49.08 21.95 47.93 0.04720 0.60 3.60 - - - - 49.06 9.93 63.19 0.078

B10 0.70 2.00 0.50 - 1.00 0.015 49.09 23.19 43.85 0.04820 0.60 3.60 0.50 - 0.10 0.025 49.08 11.34 53.34 0.081

C10 0.50 1.90 1.50 - 0.10 0.030 49.31 25.26 34.93 0.05620 0.50 1.90 3.50 - 0.10 0.005 49.41 15.80 37.23 0.084

D10 0.70 2.00 - 4.00 0.10 0.010 49.59 9.64 37.22 0.13820 0.60 3.60 - 4.00 0.80 0.010 49.56 16.38 36.46 0.083

E10 3.50 0.30 - 5.00 0.10 0.005 49.62 8.51 19.23 0.30320 3.50 0.30 - 4.50 0.50 0.050 49.58 8.81 19.51 0.288

F10 0.70 2.00 4.00 3.00 0.10 0.005 49.56 10.94 19.55 0.23220 0.60 3.60 4.50 1.50 0.10 0.010 49.43 14.84 20.90 0.159

G10 1.50 0.50 4.50 5.00 0.10 0.015 49.68 8.20 12.17 0.49820 1.50 0.50 4.00 5.00 0.10 0.015 49.69 7.56 11.80 0.557

Case A, in which the VSWT does not provide frequency regulation, is similar to the strategyproposed in [55]. It has been proven that the PSHP governor gains proposed by the authors, and thegains obtained in this study, match closely.

Energies 2018, 11, 239 13 of 25

Figure 7 shows the comparison of the quality indicators between the seven proposed cases.It can be observed that the fast frequency response elicited by the proportional controller improvesthe NADIR value, thereby reaching an even better value when it acts synergistically with inertialcontrol. In the same way, the power settling time is reduced. To reduce the frequency settling time, it isconvenient that both controls act jointly. In contrast, if only the inertial control is effective, the frequencysettling time is increased.

Energies 2018, 11, 239 12 of 24

20 3.50 0.30 ‐ 4.50 0.50 0.050 49.58 8.81 19.51 0.288

F 10 0.70 2.00 4.00 3.00 0.10 0.005 49.56 10.94 19.55 0.232

20 0.60 3.60 4.50 1.50 0.10 0.010 49.43 14.84 20.90 0.159

G 10 1.50 0.50 4.50 5.00 0.10 0.015 49.68 8.20 12.17 0.498

20 1.50 0.50 4.00 5.00 0.10 0.015 49.69 7.56 11.80 0.557

Case A, in which the VSWT does not provide frequency regulation, is similar to the strategy

proposed in [55]. It has been proven that the PSHP governor gains proposed by the authors, and the

gains obtained in this study, match closely.

Figure 7 shows the comparison of the quality indicators between the seven proposed cases. It

can be observed that the fast frequency response elicited by the proportional controller improves the

NADIR value, thereby reaching an even better value when it acts synergistically with inertial control.

In the same way, the power settling time is reduced. To reduce the frequency settling time, it is

convenient that both controls act jointly. In contrast, if only the inertial control is effective, the

frequency settling time is increased.

Figure 7. Evolution of response indicators for different cases. Blue bars represent simulations

assuming constant wind speed of 10 m/s while orange bars represent simulations assuming constant

wind speed of 20 m/s.

Although the proposed criterion does not aim towards the improvement of any particular

quality indicator, the three previously mentioned are improved. It is important to highlight the

system’s improvement by obtaining the set of gains jointly (PSHP + VSWT) rather than individually

(VSWT), comparing elicited results from cases C, E, and G, compared to B, D, and F, respectively.

Finally, the need to take into account the wind speed is verified since the latter determines the

operating point of the VSWT, and therefore the operating point of the PSHP. Once the wind speed

Figure 7. Evolution of response indicators for different cases. Blue bars represent simulations assumingconstant wind speed of 10 m/s while orange bars represent simulations assuming constant wind speedof 20 m/s.

Although the proposed criterion does not aim towards the improvement of any particular qualityindicator, the three previously mentioned are improved. It is important to highlight the system’simprovement by obtaining the set of gains jointly (PSHP + VSWT) rather than individually (VSWT),comparing elicited results from cases C, E, and G, compared to B, D, and F, respectively. Finally, the needto take into account the wind speed is verified since the latter determines the operating point of theVSWT, and therefore the operating point of the PSHP. Once the wind speed has been taken into accountin the setting of the controllers, it will not significantly affect the quality of the power system.

5.3. Simulation Results

To check the suitability of controller adjustments, Jones et al. [69] affirmed that it is enough tosimulate a step, a ramp, and a random signal. In accordance to this methodology, three differentevents related with renewable sources generation were simulated in [70]. Therefore, a load step,a wind-speed ramp (see Figure 8a) and a wind-speed fluctuation (see Figure 8b) have beensimulated. Notwithstanding, unfortunately, these results cannot be compared at the present time withexperimental data, it seems reasonable to expect a fairly good agreement, because a similar modelhas been used in [45] for Dinorwig power plant, where the simulation results reproduce the fieldmeasurements with sufficient accuracy.

Energies 2018, 11, 239 14 of 25

Energies 2018, 11, 239 13 of 24

has been taken into account in the setting of the controllers, it will not significantly affect the quality

of the power system.

5.3. Simulation Results

To check the suitability of controller adjustments, Jones et al. [69] affirmed that it is enough to

simulate a step, a ramp, and a random signal. In accordance to this methodology, three different

events related with renewable sources generation were simulated in [70]. Therefore, a load step, a

wind-speed ramp (see Figure 8a) and a wind-speed fluctuation (see Figure 8b) have been simulated.

Notwithstanding, unfortunately, these results cannot be compared at the present time with

experimental data, it seems reasonable to expect a fairly good agreement, because a similar model

has been used in [45] for Dinorwig power plant, where the simulation results reproduce the field

measurements with sufficient accuracy.

(a) (b)

Figure 8. (a) Wind speed ramp; (b) wind speed time series.

Cases from B to G have been compared with case A, and have been considered as the base case

to highlight the variation of each parameter mentioned previously. For case A, simulations with

variable wind speeds, and gains Kpw and Kiw have been extracted from [44] and assigned to 1.5 and

0.15, respectively, since they could not be extracted from the exhaustive search.

Figures 9 and 10 show the dynamic response comparison between the base case (case A) and the

different cases of VSWT contributions to frequency regulation, when a 5% power demand step is

imposed, considering constant wind speeds of 10 m/s and 20 m/s, respectively, and for the cases in

which PSHP and VSWT controller gains have been obtained jointly.

It can be verified that, regardless of the wind speed, the contribution of the VSWT to the

frequency regulation is positive for the system, since it increases the value of the NADIR reducing

the frequency and power settling time. In addition, VSWT contribution moderates the PSHP

mechanical equipment movements.

Additionally, Figure 11 also shows the dynamic response comparison between the base case

(case A) and the different cases of VSWT contributions to frequency regulation, when a 5% power

demand step is imposed, considering constant wind speed of 6 m/s and for the cases in which PSHP

and VSWT controller gains have been obtained jointly. In this low wind speed regime, the blade pitch

control does not act and the rotor speed variances are only controlled by changing generator torque.

Despite the low power generated by the VSWT due to the low wind speed, the VSWT can still

contribute to the frequency regulation by improving all the mentioned system quality indicators.

However, as can be seen in the simulation, proportional control makes the rotor speed would take

too long to recover its reference speed after the disturbance. Nevertheless, inertial control can

improve the system dynamics without compromising the stability of VSWT.

Figure 8. (a) Wind speed ramp; (b) wind speed time series.

Cases from B to G have been compared with case A, and have been considered as the base caseto highlight the variation of each parameter mentioned previously. For case A, simulations withvariable wind speeds, and gains Kpw and Kiw have been extracted from [44] and assigned to 1.5 and0.15, respectively, since they could not be extracted from the exhaustive search.

Figures 9 and 10 show the dynamic response comparison between the base case (case A) andthe different cases of VSWT contributions to frequency regulation, when a 5% power demand step isimposed, considering constant wind speeds of 10 m/s and 20 m/s, respectively, and for the cases inwhich PSHP and VSWT controller gains have been obtained jointly.

It can be verified that, regardless of the wind speed, the contribution of the VSWT to thefrequency regulation is positive for the system, since it increases the value of the NADIR reducing thefrequency and power settling time. In addition, VSWT contribution moderates the PSHP mechanicalequipment movements.

Additionally, Figure 11 also shows the dynamic response comparison between the base case(case A) and the different cases of VSWT contributions to frequency regulation, when a 5% powerdemand step is imposed, considering constant wind speed of 6 m/s and for the cases in which PSHPand VSWT controller gains have been obtained jointly. In this low wind speed regime, the bladepitch control does not act and the rotor speed variances are only controlled by changing generatortorque. Despite the low power generated by the VSWT due to the low wind speed, the VSWT canstill contribute to the frequency regulation by improving all the mentioned system quality indicators.However, as can be seen in the simulation, proportional control makes the rotor speed would take toolong to recover its reference speed after the disturbance. Nevertheless, inertial control can improve thesystem dynamics without compromising the stability of VSWT.

Energies 2018, 11, 239 15 of 25

Energies 2018, 11, 239 14 of 24

Figure 9. Comparison of the dynamic response of the system between the base case and the case in

which VSWT contributes to frequency regulation by combining the inertial and proportional control,

and by considering a sudden power demand variation and a constant wind speed of ws = 10 m/s.


which the VSWT contributes to frequency regulation by combining the inertial and proportional

control, and by considering a sudden power demand variation and a constant wind speed of ws = 20

m/s.

Figure 9. Comparison of the dynamic response of the system between the base case and the case inwhich VSWT contributes to frequency regulation by combining the inertial and proportional control,and by considering a sudden power demand variation and a constant wind speed of ws = 10 m/s.

Energies 2018, 11, 239 14 of 24


which VSWT contributes to frequency regulation by combining the inertial and proportional control,

and by considering a sudden power demand variation and a constant wind speed of ws = 10 m/s.




m/s.

Figure 10. Comparison of the dynamic response of the system between the base case and the case inwhich the VSWT contributes to frequency regulation by combining the inertial and proportional control,and by considering a sudden power demand variation and a constant wind speed of ws = 20 m/s.

Energies 2018, 11, 239 16 of 25Energies 2018, 11, 239 15 of 24




m/s.

Figure 12 shows the comparison of the dynamic responses of the system between the strategy in

which VSWT did not contribute to the regulation, and the various other strategies of contribution in

instances when a linear wind speed variation takes place.

Figure 12. Comparison of the dynamic responses of the system between the base case and the cases

in which the VSWT contributes to the regulation assuming different control strategies during a wind

speed ramp.

Figure 11. Comparison of the dynamic response of the system between the base case and the case inwhich the VSWT contributes to frequency regulation by combining the inertial and proportional control,and by considering a sudden power demand variation and a constant wind speed of ws = 6 m/s.

Figure 12 shows the comparison of the dynamic responses of the system between the strategy inwhich VSWT did not contribute to the regulation, and the various other strategies of contribution ininstances when a linear wind speed variation takes place.

Energies 2018, 11, 239 15 of 24




m/s.

Figure 12 shows the comparison of the dynamic responses of the system between the strategy in

which VSWT did not contribute to the regulation, and the various other strategies of contribution in

instances when a linear wind speed variation takes place.

Figure 12. Comparison of the dynamic responses of the system between the base case and the cases

in which the VSWT contributes to the regulation assuming different control strategies during a wind

speed ramp.

Figure 12. Comparison of the dynamic responses of the system between the base case and the casesin which the VSWT contributes to the regulation assuming different control strategies during a windspeed ramp.

Energies 2018, 11, 239 17 of 25

Table 5 summarizes the medium-frequency deviation for each strategy, calculated based onEquation (20), NADIR, maximum frequency peak, nozzle movements per second, and blade anglemovements per second when a wind ramp is simulated.

MDF =

∫ t0 |n− nre f |

t(20)

Table 5. Simulation results with a ramp wind speed.

CaseMFD NADIR Max. Frequency Peak

∫|∆z|t

∫|∆θ|t

Hz ∆ over A Hz ∆ over A Hz ∆ over A 10–5 p.u./s ∆ over A o/s ∆ over A

A 0.0195 Base 49.8719 Base 50.5947 Base 20.229 Base 0.1818 BaseB 0.0110 −43.59% 49.9997 0.26% 50.1329 −0.91% 10.171 −49.72% 0.1820 0.11%C 0.0044 −77.44% 50.0000 0.26% 50.0350 −1.11% 9.189 −54.58% 0.1844 1.43%D 0.0123 −36.92% 49.9778 0.21% 50.1683 −0.84% 11.690 −42.21% 0.1833 0.83%E 0.0077 −60.51% 49.9814 0.22% 50.1354 −0.91% 14.581 −27.92% 0.1818 0.00%F 0.0109 −44.10% 50.0000 0.26% 50.0648 −1.05% 10.052 −50.31% 0.1839 1.16%G 0.0038 −80.51% 50.0000 0.26% 50.0297 −1.12% 10.105 −50.05% 0.1832 0.77%

As shown in Figure 12, when a wind speed ramp takes place, and frequency regulation is onlyprovided by the PSHP (case A), the frequency attains values outside the limits established by the TSO(50 Hz ± 0.15 Hz) [64]. In addition, the medium frequency deviation, NADIR, maximum frequencypeak, and nozzle movement values are improved, supposing a small increase in the movements of theVSWT blades.

The elicited results from the simulation of a wind speed fluctuation are summarized inTable 6, listing for each strategy the wind energy generated, medium frequency deviation, NADIR,maximum frequency peak, nozzle movements per second, and blade angle movements per second.Moreover, Figure 13 shows the frequency comparison between cases A, C, E, and G. In addition,the dynamic responses of the system in cases A, C, E, and G during the wind speed fluctuation areshown in Appendix B.

Energies 2018, 11, 239 16 of 24

Table 5 summarizes the medium-frequency deviation for each strategy, calculated based on

Equation (20), NADIR, maximum frequency peak, nozzle movements per second, and blade angle

movements per second when a wind ramp is simulated.

MDF =∫ |𝑛 − 𝑛𝑟𝑒𝑓|

𝑡

0

𝑡 (20)

Table 5. Simulation results with a ramp wind speed.

Case MFD NADIR Max. Frequency Peak ∫|∆𝒛|

𝒕⁄

∫|∆𝜽|𝒕

⁄

Hz ∆ over A Hz ∆ over A Hz ∆ over A 10–5 p.u./s ∆ over A o/s ∆ over A

A 0.0195 Base 49.8719 Base 50.5947 Base 20.229 Base 0.1818 Base

B 0.0110 −43.59% 49.9997 0.26% 50.1329 −0.91% 10.171 −49.72% 0.1820 0.11%

C 0.0044 −77.44% 50.0000 0.26% 50.0350 −1.11% 9.189 −54.58% 0.1844 1.43%

D 0.0123 −36.92% 49.9778 0.21% 50.1683 −0.84% 11.690 −42.21% 0.1833 0.83%

E 0.0077 −60.51% 49.9814 0.22% 50.1354 −0.91% 14.581 −27.92% 0.1818 0.00%

F 0.0109 −44.10% 50.0000 0.26% 50.0648 −1.05% 10.052 −50.31% 0.1839 1.16%

G 0.0038 −80.51% 50.0000 0.26% 50.0297 −1.12% 10.105 −50.05% 0.1832 0.77%

As shown in Figure 12, when a wind speed ramp takes place, and frequency regulation is only

provided by the PSHP (case A), the frequency attains values outside the limits established by the TSO

(50 Hz ± 0.15 Hz) [64]. In addition, the medium frequency deviation, NADIR, maximum frequency

peak, and nozzle movement values are improved, supposing a small increase in the movements of

the VSWT blades.

The elicited results from the simulation of a wind speed fluctuation are summarized in Table 6,

listing for each strategy the wind energy generated, medium frequency deviation, NADIR, maximum

frequency peak, nozzle movements per second, and blade angle movements per second. Moreover,

Figure 13 shows the frequency comparison between cases A, C, E, and G. In addition, the dynamic

responses of the system in cases A, C, E, and G during the wind speed fluctuation are shown in

Appendix B.

Figure 13. Frequency comparison between cases A, C, E, and G during wind speed fluctuation.

Figure 13. Frequency comparison between cases A, C, E, and G during wind speed fluctuation.

Energies 2018, 11, 239 18 of 25

Table 6. Simulation results using variable wind speeds.

CaseWind Energy MFD NADIR Maximum Frequency Peak

∫|∆z|t

∫| ∆θ|t

MWh ∆ over A Hz ∆ over A Hz ∆ over A Hz ∆ over A 10–5 p.u./s ∆ over A o/s ∆ over A

A 2.6707 Base 0.0400 Base 49.677 Base 50.2781 Base 46.493 Base 0.0800 BaseB 2.6686 −0.08% 0.0119 −71.75% 49.715 0.08% 50.0967 −0.36% 11.340 −75.61% 0.0874 9.25%C 2.6616 −0.34% 0.0030 −92.50% 49.927 0.50% 50.0521 −0.45% 6.7713 −85.44% 0.0854 6.75%D 2.6697 −0.04% 0.0133 −66.75% 49.773 0.19% 50.1780 −0.20% 13.966 −69.96% 0.0856 7.00%E 2.6701 −0.02% 0.0102 −74.50% 49.837 0.32% 50.1101 −0.33% 19.375 −58.33% 0.0858 7.25%F 2.6644 −0.24% 0.0069 −82.75% 49.809 0.27% 50.0539 −0.45% 6.7310 −85.52% 0.0863 7.88%G 2.6658 −0.18% 0.0031 −92.25% 49.908 0.46% 50.0288 −0.50% 8.3311 −82.08% 0.0874 9.25%

As seen in Table 6, the VSWT contribution to frequency regulation implies a negligible loss of windenergy (less than 0.25%). Nevertheless, the medium frequency deviation, NADIR, maximum frequencypeak and nozzle movement values are improved.

In both simulations assuming variances in wind speed, it is verified that for the proposed cases,the VSWT contribution to frequency regulation implies an improvement in the frequency indicators ofthe quality system. In regard to the moving parts, an important reduction in the movements of theturbine nozzle (more than 80%) takes place, thereby increasing its remaining lifetime. These reductionsin movements suppose a small increase (less than 10%) in the movements of the VSWT blades.It can be observed that emulation of inertia improves the minimum and maximum frequency peaksas well as the medium frequency deviation in a better manner compared to proportional control.More importantly, these indicators reach an even better value when proportional control acts togetherwith inertial control. The system improvement is also evaluated by obtaining the set of combined gains(PSHP + VSWT) instead of individually gains when wind variation is simulated comparing resultsfrom cases C, E, and G, to those from B, D, and F, respectively, in both simulations assuming variancesin wind speed.

6. Conclusions

In this study, the capacity of a hybrid wind–hydro power plant to contribute to frequencyregulation in an isolated system has been evaluated. To achieve this, a PSHP operating in generationmode, and VSWT connected to an isolated system, have been modeled.

In addition to the frequency regulation, usually provided by the hydroelectric power plant,VSWT can contribute to frequency regulation according to different proposed control strategies,including inertial, proportional, and their combination. To the author’s knowledge, there is no controlstrategies for VSWT to contribute to frequency regulation in conjunction with a hydroelectric plant inan isolated system proposed previously. It has been proven that VSWT controller gains recommendedfor interconnected systems are not adequate for isolated systems, since isolated systems are moresensitive to power disturbances than interconnected systems. Therefore, a methodology based onexhaustive searches for the set of gains for the PSHP and VSWT controllers has been conductedaccording to a proposed criterion. The convenience of adjusting jointly PSHP and VSWT regulatorsand taking into account the wind speed regime has been demonstrated.

Control strategies and adjustment methodology extracted from this study have been appliedto the El Hierro power system, evaluating by simulating different events related to fluctuations inwind speed, or variations in power demand. Considerable improvements concerning frequencydeviations have been achieved. When a load step occurs, the fast frequency response provided by theproportional controller improves the NADIR value, thereby reaching an even better value when itacts synergistically with inertial control. Nevertheless, inertial control improves the minimum andmaximum frequency peaks as well as the medium frequency deviation in a better manner compared toproportional control when wind speed variations are simulated. For both disturbances, better qualityindicators were achieved even when proportional control acted together with the inertial control.In addition, wind energy lost owing to the VSWT contribution to frequency regulation could beconsidered negligible.

Energies 2018, 11, 239 19 of 25

Moreover, a simulation with a low wind speed has been carried out. In this speed regime,the blade pitch control does not act and the rotor speed variances are only controlled bychanging generator torque. It has been proved that proportional control can destabilize the VSWT.Nevertheless, inertial control can improve the system dynamics without compromising the stabilityof VSWT.

Finally, it has been verified that the VSWT contribution to frequency regulation improves thelifetime of the hydro turbine governing system owing to the reduction of their movements at theexpense of an admissible and increased workload imposed on the wind turbine blades.

Acknowledgments: The work presented in the paper has been partially funded by the Spanish Ministry ofEconomy and Competitiveness under the project ‘Value of pumped-hydro energy storage in isolated powersystems with high wind power penetration’ of the National Plan for Scientific and Technical Research andInnovation 2013–2016 (Ref. ENE2016–77951–R).

Author Contributions: Guillermo Martínez-Lucas developed the wind-hydro power plant model, carried out thesimulations and collaborated in the design of the control strategies and the analysis of results. José Ignacio Sarasúacollaborated in the design of the control strategies and the analysis of results. José Ángel Sanchez-Fernándezcollaborated in the development of the simulation model blocks, which correspond to the variable speedwind turbine.

Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

Ar [m2] Area swept by rotor bladesaw [m/s] Wave speedch [p.u.] Hydraulic turbine mechanical torqueCp VSWT power coefficientD [m] Penstock diameterf Darcy–Weisbach friction factorg [m/s2] Gravity accelerationh [p.u.] Net headH [m] Net headh0 [p.u.] Initial net headHb [m] Base headhi [p.u.] Head at the end of the i-th Π element of the penstockHwt [p.u.] Wind turbine inertia constantk [p.u.] Load—self regulation coefficientKdn Constant that weights the frequency variation in the VSWTKic Integral gain in PI blade pitch angle compensationKip Integral gain in PI blade pitch angle controlKiω Integral gain in PI VSWT speed controlKpc Proportional gain in PI blade pitch angle compensationKpn Constant that weights the frequency deviation in the VSWTKpp Proportional gain in PI blade pitch angle controlKpω Proportional gain in PI VSWT speed controlL [m] Penstock lengthLe [m] Segment lengthMFD Mean frequency deviationn [p.u.] Frequencyn0 [p.u.] Initial frequencynref [p.u.] Reference frequencynt Number of segments in which the penstock is dividedp0

d [MW] Initial power demandpdem [p.u.] Power demandpdn [p.u.] Power reference provided by VSWT inertial controlph [p.u.] Power supplied by PSHP

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p0h [MW] Initial power supplied by PSHP

pn [p.u.] Power reference provided by VSWT proportional and inertial controlpnc [p.u.] Power supplied by VSWT converterp0

nc [p.u.] Initial power supplied by VSWT converterp0

nc [MW] Initial power supplied by VSWT converterppn [p.u.] Power reference provided by VSWT proportional controlpwind [p.u.] Wind mechanical powerpω [p.u.] Power reference provided by VSWT speed controlq [p.u.] Flow through the turbineQb [m3/s] Base flowQp [m3/s] Flow at the penstockqp [p.u.] Flow at the penstockqp,i [p.u.] Flow at the end of the i-th Π element of the penstockq0

p [p.u.] Initial flow at the penstockr/2 [p.u.] Continuous head losses coefficient in the penstockRb [m] VSWT radiusS [m2] Penstock sectionsw [m/s] Wind speedt [s] TimeTe [s] Water elastic time (L/aw)Tl =Te

2/Tw

Tm [s] Mechanical starting timeTn [s] Frequency settling timeTp [s] Power settling timeTr [s] Hydro governor dashpot time constantTs [s] Time constant in servo motor transfer functionTw [s] Penstock water starting timex [m] axial distance along the streamlinez [p.u.] Nozzle openingz0 [p.u.] Initial nozzle openingαij Cp curves coefficientsδ Hydro governor temporary speed droopθ [o] VSWT blade pitch angleθ0 [o] VSWT initial blade pitch angleθmax [o] VSWT maximum blade pitch angleλ Ratio of the rotor blade tip speed and the wind speedρ [kg/m3] Air density: 1.225 kg/m3

ϕ Coefficient proposedω [p.u.] VSWT rotational rotor speedΩ [rad/s] VSWT rotational rotor speedω0 [p.u.] Initial VSWT rotational rotor speedωref [p.u.] Reference VSWT rotational rotor speed

Appendix A

Table A1. Cp coefficients αij.

α00 −4.1909 × 10−1 α01 2.1808 × 10−1 α02 −1.2406 × 10−2 α03 −1.3365 × 10−4 α04 1.1524 × 10−5

α10 −6.7606 × 10−2 α11 6.0405 × 10−2 α12 −1.3934 × 10−2 α13 1.0683 × 10−3 α14 −2.3895 × 10−5

α20 1.5727 × 10−2 α21 −1.0996 × 10−2 α22 2.1495 × 10−3 α23 −1.4855 × 10−4 α24 2.7937 × 10−6

α30 −8.6018 × 10−4 α31 5.7051 × 10−4 α32 −1.0479 × 10−4 α33 5.9924 × 10−6 α34 −8.9194 × 10−8

α40 1.4787 × 10−5 α41 −9.4839 × 10−6 α42 1.6167 × 10−6 α43 −7.1535 × 10−8 α44 4.9686 × 10−10

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Table A2. Blade pitch angle control parameters.

Kpc 3 Kpp 150 θmax 27Kic 30 Kip 25 Ts 0.1

Appendix B

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Appendix B

Figure A1. Dynamic responses of the system in case A during wind speed fluctuation.

Figure A2. Dynamic responses of the system in case C during wind speed fluctuation.


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Appendix B


Figure A2. Dynamic responses of the system in case C during wind speed fluctuation. Figure A2. Dynamic responses of the system in case C during wind speed fluctuation.

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Figure A3. Dynamic responses of the system in case E during wind speed fluctuation.

Figure A4. Dynamic responses of the system in case G during wind speed fluctuation.

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